Math A day in the life of a research mathematician

Hi all,
I'll be starting my final year of my undergraduate degree in pure mathematics next year. My intention is to do postgraduate work and then try to get a position as a research fellow. However, I don't really know what a research mathematician does on a day to day basis, I just like the idea of being paid to do mathematics. Would anyone care to enlighten me? Also, is it hard to find research positions at universities and is it common practice for researchers to teach?
Thanks.

* pondering my proofs, revising them when I find errors or better ways of doing them, checking them and checking them and checking them again.

* writing papers, writing notes for my self.

* going to seminars by people, giving some myself sometimes.

* chatting over coffee with people in the department - this is very important.

Some days I feel depressed and disillusioned and get very little work done. Other times I feel inspired and work from early till late and don't want to stop. Sometimes I work very odd hours. I try to take breaks and go for walks during the day.

Since when I want to get my next job, I'll judged on my published papers and it is quite competitive, there is a fair amount of pressure to get things done. But the future is uncertain in research work (at least for me), so personally I spend a fair amount of time worrying.

Soon I will be adding "writing applications for grants, etc.", and "applying for my next job" to the list, but at the moment I am just concentrating on getting some research done. I don't really know what happens further along.

A disclaimer:
* I think maybe I am not very good at mathematics, even after finishing my PhD, so it is possible other research mathematicians are doing more exciting things with their time and never have to worry about anything.

* pondering my proofs, revising them when I find errors or better ways of doing them, checking them and checking them and checking them again.

* writing papers, writing notes for my self.

* going to seminars by people, giving some myself sometimes.

* chatting over coffee with people in the department - this is very important.

Some days I feel depressed and disillusioned and get very little work done. Other times I feel inspired and work from early till late and don't want to stop. Sometimes I work very odd hours. I try to take breaks and go for walks during the day.

Since when I want to get my next job, I'll judged on my published papers and it is quite competitive, there is a fair amount of pressure to get things done. But the future is uncertain in research work (at least for me), so personally I spend a fair amount of time worrying.

Soon I will be adding "writing applications for grants, etc.", and "applying for my next job" to the list, but at the moment I am just concentrating on getting some research done. I don't really know what happens further along.

A disclaimer:
* I think maybe I am not very good at mathematics, even after finishing my PhD, so it is possible other research mathematicians are doing more exciting things with their time and never have to worry about anything.

RE: your disclaimer.

I don't think it's possible for you to not be very good at mathematics with a Ph.D in it. You may not be a Gauss or anything, but it's not possible for someone not very good at mathematics to get a Ph.D in mathematics.